Purpose: Decision-analytic models of cancer screening and treatment must include sub-models of cancer survival post diagnosis. One simple model postulates a probability p of permanent cure and an excess annual mortality rate m for those not permanently cured. Analysts can choose a combination (p,m) to accurately fit cause-specific survival data from the SEER cancer registry. However, if a model sensitivity analysis on (p, m) is desired, it is not obvious what neighborhood of the estimated (p,m) should be explored. We address this question by using Bayesian analysis to derive the approximate posterior distribution of (p,m) given survival data.
Methods: Bayesian theory states that the large-sample posterior distribution of (p,m) is approximately bivariate normal with mean equal to the posterior mode and covariance matrix equal to the Hessian of the log-posterior density. This approximate posterior distribution can be used to guide a sensitivity analysis.
Results and conclusions: For stage-II ovarian cancer, the posterior distribution of (p,m) given SEER survival data is approximately bivariate normal with mean/SD equal to 0.423/0.048 for p and 0.149/0.020 for m, and correlation 0.859. For sensitivity analysis, a representative one-dimensional (p,m)-neighborhood can be explored by varying the largest principal component of this distribution within 2 SDs of its mean with the smaller principal component fixed at its mean. The band about the resulting survival curve for a 50-year-old white female is shown below. We present like results for other stages of ovarian cancer. | m |  p |  |
